LOW DIMENSIONAL SIGMA MODELS AN.D THEIR SUPERSYMMETRIC EXTENSIONS

Abstract

Low dimensional models are generally regarded to be a convenient theoretical laboratory for studying various aspects of elementary particle theory. In pa.Iticular, for two (Euclidea11) dimensions several classes of models have been proposed na.Inely, O(N) non-linear sigma models, the principal or U(N) chiral models, the CP N-l non-linear sigma models a11d the complex Grassma.Imia.Il sigma models. All of these models a1•e good examples for field theories with non-trivial dyna.Ilucal content wluch has geometric origin a11d they a1•e in many aspects closely related to non­ Abelia.I1 gauge theories. After ail introduction to the subject we give in chapter 2 a detailed formulation of various types of purely boson sigma models in two­ dimensional Euclidea11 space a11d also of their supersynunetric (Susy) extensions. The defining equations and the general insta.Ilton and non­ insta.I1ton solutions for each type of both purely boson a11d Susy models a1•e discussed. Because of the case with wluch explicit solutions ca11 be •constructed, the CP N-'non-linear sigma models offer a good theoretical laboratmy for clarifying non-linear interactions in pa.Iticle physics.